How can marginal cost be used to calculate the cost of increasing production?

[Kuma]

Homework Statement

If you are given the marginal cost function: C'(q) and the problem asks what would the cost be to increase production from x units to y units, then, would that just be given by c'(y) - c'(x)
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Homework Equations

The Attempt at a Solution

Not entirely sure about this problem, but since marginal cost is = to the cost of producing one extra good, then it seems that would make sense, but i just need clarification to whether we need the TC (Total cost) function as well?

 

[mighty2000]

Your approach is correct. The marginal cost function, C'(q), represents the cost of producing one additional unit. Therefore, to find the cost of increasing production from x units to y units, you would simply subtract the marginal cost at y units from the marginal cost at x units, as you suggested. There is no need for the total cost function in this scenario.

It is important to note, however, that the marginal cost function may not be constant and may change as production increases. In this case, you would need to integrate the marginal cost function over the range of x to y units to find the total cost of increasing production. But if the marginal cost function is constant, then your approach is correct.

I hope this clarifies your doubts. Keep up the good work!